with \(r = \sqrt{\left(x-x_0\right)^2 + \left(y-y_0\right)^2}\)  denoting the radial coordinate and \(\beta \)  being the vortex strength. As
explained in [1]}, however, in order to emphasize the role of the Mach number \(Ma\) , we define
\(\delta T = \frac{1-\gamma }{8\gamma \pi ^2}Ma^2\beta ^2e^{1-r^2}\) 
